How to write a logical fallacy essay for math

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Writing a Paper: Avoiding Logical Fallacies This guide includes instructional pages on the writing process.

Overview

Logical fallacies are errors of reasoning—specific ways in which arguments fall apart due to faulty connection making. While logical fallacies may be used intentionally in certain forms of persuasive writing (e.g., in political speeches aimed at misleading an audience), fallacies tend to undermine the credibility of objective scholarly writing. Knowledge of how successful arguments are structured, then—as well as of the different ways they may fall apart—is a useful tool for both academic reading and writing. If you are writing an annotated bibliography or literature review, for instance, being able to recognize logical flaws in others‘ arguments may enable you to critique the validity of claims, research results, or even theories in a particular text. Along the same lines, if you are putting together your own argumentative paper (KAM, dissertation proposal, prospectus, etc.), understanding argument structure and fallacies will help you avoid errors of reasoning in your own work.

Argument Structure

The basic structure of all arguments involves three interdependent elements:

  1. Claim (also known as the conclusion)—What you are trying to prove. This is usually presented as your essay‘s thesis statement.
  2. Support (also known as the minor premise)—The evidence (facts, expert testimony, quotes, and statistics) you present to back up your claims.
  3. Warrant (also known as major premise)—Any assumption that is taken for granted and underlies your claim.

Consider the claim, support, and warrant for the following examples:

Claim: The No Child Left Behind Act (NCLB, 2001) has led to an increase in high school student drop-out rates.

Support: Drop-out rates in the US have climbed by 20% since 2001.

Warrant: (The claim presupposes that) it‘s a "bad" thing for students to drop out.

Claim: ADHD has grown by epidemic proportions in the last 10 years

Support: In 1999, the number of children diagnosed with ADHD was 2.1 million; in 2009, the number was 3.5 million.

Warrant: (The claim presupposes that) a diagnosis of ADHD is the same thing as the actual existence of ADHD; it also presupposes that ADHD is a disease.

Claims fall into three categories: claims of fact, claims of value, and claims of policy. All three types of claims occur in scholarly writing although claims of fact are probably the most common type you will encounter in research writing. Claims of fact are assertions about the existence (past, present, or future) of a particular condition or phenomenon:

Example: Japanese business owners are more inclined to use sustainable business practices than they were 20 years ago.

The above statement about Japan is one of fact; either the sustainable practices are getting more popular (fact) or they are not (fact). In contrast to claims of fact, those of value make a moral judgment about a phenomenon or condition:

Example: Unsustainable business practices are unethical.

Notice how the claim is now making a judgment call, asserting that there is greater value in the sustainable than in the unsustainable practices. Lastly, claims of policy are recommendations for actions—for things that should be done:

Example: Japanese carmakers should sign an agreement to reduce carbon emissions in manufacturing facilities by 50% by the year 2025.

The claim in this last example is that Japanese carmakers‘ current policy regarding carbon emissions needs to be changed.

For the most part, the claims you will be making in academic writing will be claims of fact. Therefore, examples presented below will highlight fallacies in this type of claim. For an argument to be effective, all three elements—claim, support, and warrant—must be logically connected.

Fallacies

Although there are more than two dozen types and subtypes of logical fallacies, many of these are likelier to occur in persuasive, rather than expository or research, writing. Below are the most common forms of fallacy that you may encounter in the type of expository/research writing you are apt to do at Walden:

Example: Special education students should not be required to take standardized tests because such tests are meant for nonspecial education students.

Example: Two out of three patients who were given green tea before bedtime reported sleeping more soundly. Therefore, green tea may be used to treat insomnia.

Example: Professor Berger has published numerous articles in immunology. Therefore, she is an expert in complementary medicine.

Example: Drop-out rates increased the year after NCLB was passed. Therefore, NCLB is causing kids to drop out.

Example: Japanese carmakers must implement green production practices, or Japan‘s carbon footprint will hit crisis proportions by 2025.

In addition to claims of policy, false dilemma seems to be common in claims of value. For example, claims about abortion‘s morality (or immorality) presuppose an either-or about when "life" begins. Our earlier example about sustainability ("Unsustainable business practices are unethical.") similarly presupposes an either/or: business practices are either ethical or they are not, it claims, whereas a moral continuum is likelier to exist.

Wrap Up

As you can see from the examples above, there are many ways arguments can fall apart due to faulty connection making. When trying to induce inferences from data, for instance, it‘s important not to draw conclusions too quickly or too globally; otherwise, you may end up with errors of hasty or sweeping generalization that will weaken your overall thesis. Similarly, it‘s important not to construct an either-or argument when dealing with a complex, multi-faceted issue or to assume a causal relationship when dealing with a merely temporal one; the ensuing errors—false dilemma and post hoc ergo procter hoc, respectively—may weaken argument as well. Being attentive to logical fallacies in others‘ writings will make you a more effective "critic" and writer of literature review assignments, annotated bibliographies and article critiques. Being attentive to fallacies in your own writing will help you build more compelling arguments, whether putting together a dissertation prospectus or simply writing a short discussion post on the applications of a particular theory.